In recent years, a number of theoretical models have been developed
at Iowa State University to predict the electrical voltage signals
seen during ultrasonic inspections of metal components. For example,
the Thompson-Gray measurement model can predict the absolute voltage
of the echo from a small defect, given information about the host
metal (information such as density, sound speeds, surface curvature,
etc.), the defect (size, shape, location, etc.), and the inspection
system (water path, transducer characteristics, reference echo
from a calibration block, etc.). If an additional metal property
which characterizes the inherent noisiness of the metal microstructure
is known, the independent scatterer model can be used to predict
the absolute root-mean-squared (rms) level of the ultrasonic grain
noise seen during an inspection. By combining the two models,
signal-to-noise
(S/N) ratios can be calculated.

Accurate model calculations often require intensive computer
calculations. However, by making a number of approximations in
the formalism, it is possible to obtain rapid first-order estimates
of noise levels and S/N ratios. These calculations are for normal-incidence pulse-echo
inspections through flat or curved surfaces, and
the flaw may be a flat crack or a spherical inclusion. The figure below shows the results of one of the calculations.